4. Consider the following endogenous growth model: a representative household's life-timeutility function is given as:pe C(t)!-o – 1-dt.1- 0The production function is:Y (t) = AK(t)ª Hp(t)'-awhere Hp(t) denotes human capital used in production. Human capital accumulationequation is:Н() — ВНE() — 6H(),where HE(t) is human capital devoted to education. In total we have HE(t) + Hp(t)H(t). Denote the fraction of human capital allocated to production by ø(t). Please go asfar as you can to characterize the balanced growth path of the economy.

Paul Romer in 1986 modified the AK model by creating a Ramsey version. He gave the inter temporal…

4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: The production function is: Le t=0 -pt c(t)1-0 1-0 - 1 -dt. Y(t) = AK(t)ªH₂(t)1-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is:

4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: The production function is: Le t=0 -pt c(t)1-0 1-0 - 1 -dt. Y(t) = AK(t)ªH₂(t)1-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is:

Economics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506725

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter27: Investment, The Capital Market, And The Wealth Of Nations

Section: Chapter Questions

Problem 3CQ

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Question

4. Consider the following endogenous growth model: a representative household's life-time
utility function is given as:
pe C(t)!-o – 1
-dt.
1- 0
The production function is:
Y (t) = AK(t)ª Hp(t)'-a
where Hp(t) denotes human capital used in production. Human capital accumulation
equation is:
Н() — ВНE() — 6H(),
where HE(t) is human capital devoted to education. In total we have HE(t) + Hp(t)
H(t). Denote the fraction of human capital allocated to production by ø(t). Please go as
far as you can to characterize the balanced growth path of the economy.

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